Correct brain function requires correct brain wiring. An important step in the establishment of appropriate connectivity is the guidance of axons over long distances in the developing brain to find their correct targets. A crucial type of guidance cue axons use is concentration gradients of attractive or repellent factors. Over the past decade many new molecules have been discovered that guide axons in this way. However, as yet we still have very little understanding of the precise mechanisms by which axons detect and respond to gradients. A better understanding of these mechanisms would enable us to understand better (1) how the nervous system is normally constructed, (2) why axons sometimes mistarget during development, (3) the effect of gene deletions and mutations on wiring, and (4) how to encourage axonal regeneration to appropriate targets after injury. The goal of this project is to develop a mechanistic understanding of axonal behavior in gradients by building computational models of gradient detection and directed movement for axons. Two types of models will be investigated. The first type is based on the idea that gradient detection is limited by inevitable stochastic noise in the receptor binding process. These models assume a small, spherical sensing device, and make predictions about the minimum detectable gradient steepness that such sensing devices can detect. The second type of model addresses the unique role that filopodia play in axonal gradient sensing and movement. The model is based on the idea that filopodia act as somewhat independent sensing devices, and it is their combined dynamics that determines the threshold for gradient detection and the trajectories that axons follow. A crucial component of the project is that the computational modeling will be directly tested and constrained using a new, quantitative experimental assay the investigators have recently developed. The assay allows stable molecular gradients of precisely controlled shape to be established in a collagen gel. The system used will be the guidance of dorsal root ganglion axons by gradients of Nerve Growth Factor (NG). Exponentially-shaped gradients of varying steepness of NG will be used to determine the minimum gradient steepness axons can detect as a function of absolute concentration, and the trajectories of axons in these gradients will be quantitatively analyzed.